TY - JOUR
T1 - On two nonlinear biharmonic evolution equations
T2 - Existence, uniqueness and stability
AU - Lai, Ming Jun
AU - Liu, Chun
AU - Wenston, Paul
PY - 2004/6
Y1 - 2004/6
N2 - We study the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: (Formula presented.) and (Formula presented.) with an initial value and a Dirichlet boundary conditions. We show the existence and uniqueness of the weak solutions of these two equations. For any t ∈ [0, + ∞), we prove that both solutions are in (Formula presented.). We also discuss the asymptotic behavior of the solutions as time goes to infinity. This work lays the ground for our numerical simulations for the above systems [M.J. Lai, C. Liu and P. Wenston (2004). Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations. Applicable Analysis, 83, 563–577].
AB - We study the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: (Formula presented.) and (Formula presented.) with an initial value and a Dirichlet boundary conditions. We show the existence and uniqueness of the weak solutions of these two equations. For any t ∈ [0, + ∞), we prove that both solutions are in (Formula presented.). We also discuss the asymptotic behavior of the solutions as time goes to infinity. This work lays the ground for our numerical simulations for the above systems [M.J. Lai, C. Liu and P. Wenston (2004). Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations. Applicable Analysis, 83, 563–577].
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U2 - 10.1080/00036810410001647126
DO - 10.1080/00036810410001647126
M3 - Article
AN - SCOPUS:82155194667
SN - 1522-6514
VL - 83
SP - 541
EP - 562
JO - International Journal of Phytoremediation
JF - International Journal of Phytoremediation
IS - 6
ER -